Details

sample384.0ms

Algorithm

intervals

Results

108.0ms	25×	body	5120	valid
91.0ms	60×	body	2560	valid
91.0ms	116×	body	1280	valid
52.0ms	93×	body	640	valid
11.0ms	32×	body	320	valid
8.0ms	69×	body	80	valid
3.0ms	13×	body	160	valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	44	13
1	147	13
2	857	12
3	5002	11

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.6b	(* (pow t 3.0) (tan k))
21.7b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
29.5b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

337×	`add-exp-log`
220×	`prod-exp`
71×	`div-exp`
65×	`add-cbrt-cube`
51×	`pow-exp`
34×	`pow-to-exp` `cbrt-unprod`
30×	`unpow-prod-down`
28×	`add-sqr-sqrt`
24×	`associate-l`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
12×	`cbrt-undiv`
5×	`pow1` `associate-*r/`
4×	`associate-r` `add-log-exp` `sqr-pow`
3×	`tan-quot` `pow-unpow` `div-inv` `unswap-sqr`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `associate-/l*`

Counts

4 → 179

Calls

4 calls:

4.0ms	(pow (/ k t) 2.0)
6.0ms	(* (pow t 3.0) (tan k))
44.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
20.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series902.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ k t) 2.0)
236.0ms	(* (pow t 3.0) (tan k))
362.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
240.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify134.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	974	1954
1	4995	1620
2	5001	1620

prune443.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 23.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
5.4b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.8b	(* (pow k 2.0) (pow t 1.0))
16.8b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

1597×	`add-exp-log`
1095×	`prod-exp`
882×	`pow-exp`
668×	`div-exp`
492×	`pow-to-exp`
130×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
32×	`unpow-prod-down`
20×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
19×	`times-frac` `associate-r`
18×	`associate-l`
14×	`sqr-pow`
12×	`unswap-sqr`
8×	`associate-/r*`
6×	`cbrt-unprod`
5×	`pow1`
4×	`cbrt-undiv` `unpow2` `add-log-exp`
3×	`pow-unpow` `div-inv`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-r/` `clear-num` `associate-/l`

Counts

4 → 567

Calls

4 calls:

1.0ms	(pow (sin k) 2)
6.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.0ms	(* (pow k 2.0) (pow t 1.0))
36.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin k) 2)
87.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
330.0ms	(* (pow k 2.0) (pow t 1.0))
645.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify144.0ms

Algorithm

egg-herbie

Counts

579 → 579

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	1180	6917
1	3731	6762
2	5003	6761

prune593.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
0.4b	(pow (sin k) 2)
5.4b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.8b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite288.0ms

Algorithm

rewrite-expression-head

Rules

5603×	`add-exp-log`
4515×	`prod-exp`
3078×	`pow-exp`
2032×	`div-exp`
1869×	`pow-to-exp`
434×	`rec-exp` `1-exp`
27×	`add-cbrt-cube`
23×	`add-sqr-sqrt`
22×	`times-frac`
20×	`unpow-prod-down`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
11×	`associate-l`
9×	`associate-/r*`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1` `sqr-pow`
4×	`div-inv` `associate-/l*` `unpow2` `add-log-exp`
3×	`pow-unpow` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `associate-r/` `-commutative` `inv-pow`

Counts

4 → 1460

Calls

4 calls:

20.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.0ms	(pow (sin k) 2)
6.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
61.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

336.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
20.0ms	(pow (sin k) 2)
88.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
660.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify280.0ms

Algorithm

egg-herbie

Counts

1472 → 1472

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	1742	23543
1	4574	19111
2	5002	17858

prune759.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 14.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos k) (/ (/ (sin k) l) l))
0.3b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.9b	(/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k))
16.8b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k)))

rewrite504.0ms

Algorithm

rewrite-expression-head

Rules

3522×	`times-frac`
2743×	`add-exp-log`
1561×	`add-sqr-sqrt`
1506×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp`
1348×	`div-exp`
974×	`pow-exp`
509×	`pow-to-exp`
406×	`associate-r`
186×	`rec-exp` `1-exp`
140×	`associate-/l*`
112×	`div-inv`
56×	`add-cbrt-cube`
47×	`associate-/r*`
29×	`cbrt-undiv`
15×	`unswap-sqr`
12×	`unpow-prod-down`
11×	`associate-l`
8×	`associate-/r/` `cbrt-unprod`
6×	`sqr-pow`
5×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`pow-flip` `associate-r/` `-commutative` `associate-/l/` `inv-pow`

Counts

4 → 1791

Calls

4 calls:

13.0ms	(/ (cos k) (/ (/ (sin k) l) l))
24.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
41.0ms	(/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k))
212.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k)))

series1.2s

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (cos k) (/ (/ (sin k) l) l))
336.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
88.0ms	(/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k))
663.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (sin k) l) l)) (sin k)))

simplify328.0ms

Algorithm

egg-herbie

Counts

1803 → 1803

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5001	34093

prune7.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.0b

regimes286.0ms

Accuracy

13.8% (2.9b remaining)

Error of 10.8b against oracle of 7.9b and baseline of 11.2b

bsearch647.0ms

Steps

Iters	Range		Point
10	-1.1549747614155664e-91	-4.809581082357105e-102	-1.856992087426494e-100
7	-5.136766128027413e+148	-1.1919610862734025e+147	-6.290931522942836e+147

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	58
1	61	58

end0.0ms

sample13.9s

Algorithm

intervals

Results

4.1s	2195×	body	2560	valid
3.8s	911×	body	5120	valid
3.3s	4022×	body	1280	valid
1.5s	2518×	body	640	valid
374.0ms	1054×	body	320	valid
237.0ms	2002×	body	80	valid
105.0ms	443×	body	160	valid